Question

Suppose a child swings around her straight arm counterclockwise about her shoulder joint. If her arm is 40.0 cm long, and her arm completes exactly 2 revolutions in 0.95 s, what is her arm's angular velocity in rad/s? and this one Suppose a child starts swinging around her straight arm counterclockwise about her shoulder joint, starting at rest. If her arm's angular speed reaches 13 rad/s in 1.5 seconds, what is her arm's angular acceleration in rad/s2?

Answer 1

Answer:

A. the angular velocity is 13.2 rad/seconds

B. The angular acceleration is $8.67 rad/s^{2}$

Explanation:

A

The angular velocity of the swinging arm can be calculated using the formula:

$\omega =\frac{\theta}{t}$

in our case the angular displacement,  $\theta = \frac{2\times 2\pi \times r}{r}= 4\pi radians$

time, t = 0.95 seconds

Therefore, angular velocity =$\frac{4 \pi}{0.95}=13.2 rad/s$

B.

Since the arm starts swinging from rest, the angular velocity of the arm at that point is zero.

The angular acceleration can be calculated using the formula:

$\alpha = \frac{d\omega}{dt} = \frac{13 - 0}{1.5}= 8.67 rad/s^{2}$

hence, the angular acceleration $8.67 rad/s^{2}$